The present invention relates to modems and, more particularly, to techniques for generating a modem line probing signal suitable for analyzing the characteristics of telephone lines. Apparatus for generating line probing signals have been used in the past. For example, in the book entitled Modem Handbook for the Communications Professional by Cass Lewart, on pages 258-260, the author describes a Peak-to-Average Ratio ("PAR") meter. The meter uses a PAR signal consisting of 16 harmonically unrelated sine waves of different amplitudes. The receiver portion of the instrument is said to compute the ratio of the received peak energy to average energy. This ratio is said to relate to both attenuation and delay distortion and is said to give an indication of the circuit quality. According to the author, the readings are most sensitive to envelope delay, noise, and attenuation distortion, but will not indicate which particular parameter is at fault. A PAR reading which differs by at least four units from a previous reading is said to indicate some problem on the transmission line and should be followed by more detailed testing.
An article entitled "On Minimizing the Peak-to-Average Power Ratio for the Sum of N Sinusoids" by D. R. Gimlin and C. R. Patisaul that is printed in 41 IEEE Transactions on Communications, p. 631-635 (Apr. 1993), discusses the phasing of equal amplitude, equally spaced N frequency sinusoids so that the peak-to-average power ratio of the sum is 2.6 decibels. Such disclosures, however, often do not show a modem that is sufficiently accurate in determining the non-linearity of the electrical characteristics of a telephone line, or that is sufficiently inexpensive, or that operates quickly enough.